Question

Aria Acoustics, Inc. (AAI), projects unit sales for a new seven-octave voice emulation implant as follows:

Year		Unit Sales
1			73,600
2			86,600
3			105,750
4			97,900
5			67,600

Production of the implants will require $1,650,000 in net working capital to start and additional net working capital investments each year equal to 20 percent of the projected sales increase for the following year. Total fixed costs are $3,500,000 per year, variable production costs are $258 per unit, and the units are priced at $384 each. The equipment needed to begin production has an installed cost of $17,100,000. Because the implants are intended for professional singers, this equipment is considered industrial machinery and thus qualifies as seven-year MACRS property. In five years, this equipment can be sold for about 25 percent of its acquisition cost. The tax rate is 23 percent the required return is 15 percent. MACRS schedule

a.	What is the NPV of the project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.	What is the IRR? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

a)		0	1	2	3	4	5
	Unit sales		73600	86600	105750	97900	67600
	Sales revenue at $384/unit		$   2,82,62,400	$   3,32,54,400	$   4,06,08,000	$   3,75,93,600	$    2,59,58,400
	Variable cost at $258/unit		$   1,89,88,800	$   2,23,42,800	$   2,72,83,500	$   2,52,58,200	$    1,74,40,800
	Fixed costs		$      35,00,000	$       35,00,000	$       35,00,000	$      35,00,000	$       35,00,000
	Depreciation		$      24,43,590	$       41,87,790	$       29,90,790	$      21,35,790	$       15,27,030	$     1,32,84,990
	NOI		$      33,30,010	$       32,23,810	$       68,33,710	$      66,99,610	$       34,90,570
	Tax at 23%		$         7,65,902	$         7,41,476	$       15,71,753	$      15,40,910	$          8,02,831
	NOPAT		$      25,64,108	$       24,82,334	$       52,61,957	$      51,58,700	$       26,87,739
	Add: Depreciation		$      24,43,590	$       41,87,790	$       29,90,790	$      21,35,790	$       15,27,030
	OCF		$      50,07,698	$       66,70,124	$       82,52,747	$      72,94,490	$       42,14,769
	Capital expenditure	$    1,71,00,000					$      -41,69,202	[See not below]
	Change in NWC	$        16,50,000	$         9,98,400	$       14,70,720	$       -6,02,880	$     -23,27,040	$      -11,89,200
	FCF	$ -1,87,50,000	$      40,09,298	$       51,99,404	$       88,55,627	$      96,21,530	$       95,73,171
	PVIF at 15%	1	0.86957	0.75614	0.65752	0.57175	0.49718
	PV at 15%	$ -1,87,50,000	$      34,86,346	$       39,31,496	$       58,22,718	$      55,01,141	$       47,59,558	$         47,51,259
	NPV	$        47,51,259
	WORKING FOR AFTER TAX SALE VALUE OF THE EQUIPMENT AT EOY 5:
	Sale value (17100000*25%)	$        42,75,000
	Book value = 17100000-13284990 =	$        38,15,010
	Gain on sale	$          4,59,990
	Tax on gain at 23%	$          1,05,798
	After tax cash flow from sale	$        41,69,202
b)	IRR:
	IRR is that discount rate for which NPV = 0. Such a discount rate is to be found out by trial and error to get 0 NPV.
	FCF	$ -1,87,50,000	$      40,09,298	$       51,99,404	$       88,55,627	$      96,21,530	$       95,73,171
	PVIF at 23%	1	0.81301	0.66098	0.53738	0.43690	0.35520
	PV at 23%	$ -1,87,50,000	$      32,59,592	$       34,36,713	$       47,58,871	$      42,03,622	$       34,00,402	$           3,09,201
	PVIF at 24%	1	0.80645	0.65036	0.52449	0.42297	0.34111
	PV at 24%	$ -1,87,50,000	$      32,33,305	$       33,81,506	$       46,44,663	$      40,69,653	$       32,65,483	$         -1,55,390
	IRR lies between 23% and 24%.
	By simple interpolation, IRR = 23%+1%*309201/(309201+155390) =			23.67%